1.

Record Nr.

UNINA9910254095003321

Autore

Assi Abdallah

Titolo

Numerical Semigroups and Applications / / by Abdallah Assi, Pedro A. García-Sánchez

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016

ISBN

3-319-41330-9

Edizione

[1st ed. 2016.]

Descrizione fisica

1 online resource (113 p.)

Collana

RSME Springer Series, , 2509-8896 ; ; 1

Disciplina

510

Soggetti

Geometry, Algebraic

Commutative algebra

Commutative rings

Algorithms

Discrete mathematics

Computer science - Mathematics

Algebraic Geometry

Commutative Rings and Algebras

Discrete Mathematics

Discrete Mathematics in Computer Science

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

1 Numerical semigroups, the basics -- 2 Irreducible numerical semigroups -- 3 Semigroup of an irreducible meromorphic series -- 4 Minimal presentations -- 5 Factorizations and divisibility.

Sommario/riassunto

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These



invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.